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Question

# The diameter of a football is 24 cm. What is the volume of air inside 50 such footballs?

A

225200π cm3

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B

105000π cm3

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C

115200π cm3

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D

15200π cm3

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Solution

## The correct option is C 115200π cm3 Given that the diameter of a football is 24 cm. ⟹Radius of the football=242=12 cm Volume of air inside a football = Volume of the sphere of radius 12 cm Note that the volume of a sphere of radius r=43πr3 Thus, volume of the sphere of radius 12 cm =43π(12)3=2304π cm3 Volume of air inside 50 such footballs =50×Volume of air inside a football=50×2304π=115200π cm3

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